A Caltech Library Service

A Consistent Reduced-Speed-of-Light Formulation of Cosmic Ray Transport Valid in Weak and Strong-Scattering Regimes

Hopkins, Philip F. and Squire, Jonathan and Butsky, Iryna S. (2021) A Consistent Reduced-Speed-of-Light Formulation of Cosmic Ray Transport Valid in Weak and Strong-Scattering Regimes. . (Submitted)

[img] PDF - Submitted Version
See Usage Policy.


Use this Persistent URL to link to this item:


We derive a consistent set of moments equations for CR-magnetohydrodynamics, assuming a gyrotropic distribution function (DF). Unlike previous efforts we derive a closure, akin to the M1 closure in radiation hydrodynamics (RHD), that is valid in both the nearly-isotropic-DF and/or strong-scattering regimes, and the arbitrarily-anisotropic DF or free-streaming regimes, as well as allowing for anisotropic scattering and transport/magnetic field structure. We present the appropriate two-moment closure and equations for various choices of evolved variables, including the CR phase space distribution function, number density, total energy, kinetic energy, and their fluxes or higher moments, and the appropriate coupling terms to the gas. We show that this naturally includes and generalizes a variety of terms including convection/fluid motion, anisotropic CR pressure, streaming, diffusion, gyro-resonant/streaming losses, and re-acceleration. We discuss how this extends previous treatments of CR transport including diffusion and moments methods and popular forms of the Fokker-Planck equation, as well as how this differs from the analogous M1-RHD equations. We also present two different methods for incorporating a reduced speed of light (RSOL) to reduce timestep limitations: in both we carefully address where the RSOL (versus true c) must appear for the correct behavior to be recovered in all interesting limits, and show how current implementations of CRs with a RSOL neglect some additional terms.

Item Type:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription Paper
Hopkins, Philip F.0000-0003-3729-1684
Squire, Jonathan0000-0001-8479-962X
Butsky, Iryna S.0000-0003-1257-5007
Additional Information:Support for PFH was provided by NSF Research Grants 1911233 & 20009234, NSF CAREER grant 1455342, NASA grants 80NSSC18K0562, HST-AR-15800.001-A. Numerical calculations were run on the Caltech compute cluster “Wheeler,” allocations FTA-Hopkins supported by the NSF and TACC, and NASA HEC SMD-16-7592. Support for JS was provided by Rutherford Discovery Fellowship RDF-U001804 and Marsden Fund grant UOO1727, which are managed through the Royal Society Te Apārangi. Data Availability Statement: The data supporting this article are available on reasonable request to the corresponding author.
Group:Astronomy Department, TAPIR
Funding AgencyGrant Number
Royal Society Te ApārangiRDF-U001804
Royal SocietyUOO1727
Subject Keywords:cosmic rays — plasmas — methods: numerical — MHD — galaxies: evolution — ISM: structure
Record Number:CaltechAUTHORS:20210323-112520656
Persistent URL:
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:108526
Deposited By: Tony Diaz
Deposited On:23 Mar 2021 19:04
Last Modified:23 Mar 2021 19:04

Repository Staff Only: item control page